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maria [59]
3 years ago
8

20 POINTS

Mathematics
2 answers:
Zepler [3.9K]3 years ago
8 0

Answer:

equivalent

not equivalent

equivalent

not equivalent

-step explanation:

RUDIKE [14]3 years ago
4 0

<em>The correct expressions are as follows:</em>

7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} Equivalent 343

7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} Not Equivalent 49

7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} Equivalent 7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}

7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} Not Equivalent 49^{\frac{2}{10}} \cdot 7^{\frac{1}{5}}

\texttt{ }

<h3>Further explanation</h3>

Let's recall following formula about Exponents and Surds:

\boxed { \sqrt { x } = x ^ { \frac{1}{2} } }

\boxed { (a ^ b) ^ c = a ^ { b . c } }

\boxed {a ^ b \div a ^ c = a ^ { b - c } }

\boxed {\log a + \log b = \log (a \times b) }

\boxed {\log a - \log b = \log (a \div b) }

<em>Let us tackle the problem!</em>

\texttt{ }

7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5}} \cdot (7^2)^{\frac{7}{5}}

7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5}} \cdot (7)^{2\times \frac{7}{5}}

7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = \boxed{7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}}

7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5} + \frac{14}{5}}

7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{15}{5}}

7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{3}

7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = \boxed{343}

\texttt{ }

<em>From the results above, it can be concluded that the correct statements are:</em>

7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} Equivalent 343

7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} Not Equivalent 49

7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} Equivalent 7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}

7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} Not Equivalent 49^{\frac{2}{10}} \cdot 7^{\frac{1}{5}}

\texttt{ }

<h3>Learn more</h3>
  • Coefficient of A Square Root : brainly.com/question/11337634
  • The Order of Operations : brainly.com/question/10821615
  • Write 100,000 Using Exponents : brainly.com/question/2032116

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Exponents and Surds

Keywords: Power , Multiplication , Division , Exponent , Surd , Negative , Postive , Value , Equivalent , Perfect , Square , Factor.

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